A bound for entire harmonic functions of three variables

Growth analysis of entire functions of two complex variables

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Residue Theorems of Harmonic Functions of Three Variables

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.  

A Lower Bound for the Gradient of ∞-harmonic Functions

We establish a lower bound for the gradient of the solution to∞-Laplace equation in a strongly star-shaped annulus with capacity type boundary conditions. The proof involves properties of the radial derivative of the solution, so that starshapedness of level sets easily follows.

A Lower Bound for the Gradient of 1-harmonic Functions

We establish a lower bound for the gradient of the solution to 1-Laplace equation in a strongly star-shaped annulus with capacity type boundary conditions. The proof involves properties of the radial derivative of the solution, so that starshapedness of level sets easily follows. x1. Introduction In this paper we deal with solutions to the 1-Laplace equation 1 u = n X i;j=1 u x i u x j u x i x ...